Title III Technology Literacy Challenge Grant

Learning Unit

Overview | Content Knowledge | Essential Questions | Connection To Standards | Initiating Activity | Learning Experiences | Culminating Performance | Pre-Requisite Skills | Modifications | Schedule/Time Plan | Technology Use

LU Title: What's A Problem?

Author(s): Kimberly Wells

Grade Level: 5

School : Sylvan-Verona Beach Elementary

Topic/Subject Area: Math

Address: PO Box 246 

Verona Beach, NY 13162

Email: kwells@oneida-beach.moric.org

Phone/Fax: 315-762-4404

OVERVIEW

  This three week integrated unit incorporates standards from MST and ELA. At the end of the unit, students will participate in a problem solving activity with their parent or guardian. Students will use skills learned throughout the unit while parents will use strategies that were taught at a parent workshop to complete the culminating task. Students are responsible not only to solve problems correctly; they are responsible to give written explanations of their solutions.
 
 

CONTENT KNOWLEDGE

Declarative

Students will:

Procedural

Students will:

Learn 7 problem solving strategies

Utilize strategies to solve a variety of problems 

 Explain when a specific problem solving strategy would be used

 Create problems that are solved using a particular strategy

 Understand why one strategy would be used instead of another

 Provide written explanations of problem solutions

 Understand how these strategies can be used to solve real life problems

 Work cooperatively with peers and parents

 Understand parts necessary to solve problems successfully

 Use a checklist for self evaluation

 

 

ESSENTIAL QUESTIONS
1.How can everyday materials be used to solve real life problems?
2. Why is it important to be able to solve the same problem a variety of ways?
3.Why is it important to have several ways to solve problems?

CONNECTIONS TO NYS LEARNING STANDARDS
List Standard # and Key Idea #: Write out related Performance Indicator(s) or Benchmark(s)

MST
Standard 1 - Analysis, Inquiry, and Design
Students will use mathematical analysis, scientific inquiry, and engineering design, as appropriate, to pose questions, seek answers, and develop solutions.

Standard 2 - Information Systems
Students will access, generate, process, and transfer information using appropriate technologies.

Standard 3 - Mathematics
Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real-world settings, and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability, and
trigonometry.

ELA
Standard 1 Listening and Reading

 Standard 1 Speaking and Writing


 
  INITIATING ACTIVITY

 Students will be given a task to complete (see initiating activity attachment). Put students on the clock and explain that they have to solve problems and be able to explain how they solved them. The teacher will ask the students to share their solution and the strategies they used to solve the problems. After the discussion, chooses one or two problems and show students the solutions using 2-3 different methods. Discuss the unit that they are going to be studying, making sure to include the parent workshop component.
 
 

LEARNING EXPERIENCES
In chronological order including acquisition experiences and extending/refining
experiences for all stated declarative and procedural knowledge.

Strategies

Work Backwards, Use Objects, Draw a Picture, Make a Table, Make A List, Find a Pattern, Guess and Check

 Declarative Knowledge

What declarative knowledge should students be in the process of acquiring and integrating? AS a result of this unit, the student will know or understand…

What experiences or activities will be used to help students acquire and integrate knowledge?

What strategies will be used to help students construct meaning, organize, and/or store knowledge?

Procedural Knowledge

What procedural knowledge will students be in the process of acquiring and integrating? AS a result of the this unit, students will be able to:

What will be done to help students construct models, shape and internalize the knowledge?

Strategy #1

Guess and Check

Strategy #2

Work Backwards

Strategy #3

Find a Pattern

Strategy #4

Make a List

Strategy #5

Make a Table

 Strategy #6

Draw a Picture

 Strategy #7

Use Objects

Extending and Refining Activities

What knowledge will students be extending and refining?

  What reasoning process will they be using?

Describe what will be done.

CULMINATING PERFORMANCE
Include rubric(s)

** EXTRA EXTRA **
PROBLEMS IN HONERIESWELL
The city of Honerieswell is faced with a terrible dilemma.  IN order for the great OHERWELLS to give away the treasured foods of the city, they must find worthy candidates. You are on a mission to be a worthy candidate. In the city, you are considered to be a world class problem solver. In front of you are ten problems that the great OHERWELLS have presented you with. After carefully reading all of them, chose the five that you will solve to help solve the biggest problem, getting rid of the treasured goods. The catch, you must use a different strategy to solve each one. In the spaces below, write the problem number, the strategy you used and the process you went through. You may use pictures, lists, or written explanations to show how you solve them. Only citizens who use five of the seven problem solving strategies will be considered to receive the treasured goods. Don't be alarmed, there is enough treasure for all that accept this challenge and who successfully complete it. Good Luck and thank you for your help in solving this dilemma.
 

# of problem             Strategy                                   Solution

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Signature Required for Processing

____________________________
Notes from the GREAT OHERWELLS
 

PROBLEMS
1. Kim has coins are worth $1.17, but she can't make change for a dollar. What coins does she have?

2. Oh and Well are making final awards for the problem-solving contest. Each award has a blue and an orange ribbon on it. Each strip of ribbon is 23 cm long. How many meters will they need to make 35 awards?

3. When Chris was ten years old, he carved his girlfriend's name in the truck of the Elm Tree in his side yard, two feet above the ground. While Chris would only grow 1-2 inches a year, the tree would grow 6 inches. When Chris was 25, his new wife found the tree and saw what he had written. What height was the name on the tree?

4. Old McDonald had a farm, a wife, some horses and some geese. All together there were 24 animals living in his barn. How many geese and horses does Old McDonald have if there is a total of 62 feet seen under the stalls in the barn?

5. Complete the next 5 rows of this multiples triangle.

  1. 1
  2. 2 4

3 6 9

4 8 12 16

What is the last number in row 30?

6. Main Street Pizza was celebrating "Everyone Loves Pizza Week". They are selling one topping large pizzas for $5.00! You have decided that over the course of the week you are going to eat one of each type they make. They have 4 types of crusts plus their special thin n crispy. The toppings that are available are pineapple, pepperoni, mushroom, onion, anchovies, and sausage. How many different one topping pizzas will you have toe at this week?

7. Nichole wanted to know the age of the new Temur at the zoo. Jack, the zookeeper, told her that if she added ten years to the age of the Temur and the doubled it, the Temur would be 90 years old. How old is the Temur?

 

8. You are trying to balance a 14-pound bowling ball. Which of the following weights would you choose to balance the ball, 3 lb., 5 lb., 7 lb., 10 lb., 15 lb.? Hint: You will need to use more than one weight.

9. What two numbers form a sum of 475 and a difference of 177?

10. Find 3 numbers that when added or multiplied together, their sum and product are the same.


Problem Solving Task Evaluation Checklist

#1

Student

Parent

Teacher

Comments

Identifies strategy

 

 

 

 

Strategy fits problem

 

 

 

 

Uses strategy correctly

 

 

 

 

Explanation is clear

 

 

 

 

Parent Assistance

 

 

 

 

Neat & Organized

 

 

 

 

 

 

 

 

 

#2

Student

Parent

Teacher

Comments

Identifies strategy

 

 

 

 

Strategy fits Problem

 

 

 

 

Uses strategy Correctly

 

 

 

 

Explanation is clear

 

 

 

 

Parent Assistance

 

 

 

 

Neat & Organized

 

 

 

 

 

 

 

 

 

#3

      Student

      Parent

        Teacher

    Comments

Identifies strategy 

 

 

 

 

    Strategy fits
     Problem

 

 

 

 

Uses strategy correctly

 

 

 

 

explanation is clear

 

 

 

 

Parent Assistance

 

 

 

 

Neat & Organized

 

 

 

 

 

 

 

 

 

#4

Student

Parent

Teacher

Comments

Identifies Strategy

 

 

 

 

Strategy Fits problem

 

 

 

 

Uses strategy correctly

 

 

 

 

Explanation is Clear

 

 

 

 

Parent Assistance

 

 

 

 

Neat and Organized

 

 

 

 

 

 

 

 

 

#5

Students

Parent

Teacher

Comments

Identifies Strategy

 

 

 

 

Strategy Fits Problem

 

 

 

 

Uses strategy correctly

 

 

 

 

Explanation is clear

 

 

 

 

Parent Assistance

 

 

 

 

Neat and Organized

 

 

 

 

PRE-REQUISITE SKILLS
  Students need to know basic computation.

Students may require additional assistance in using particular strategies. This may be done with the help of other students, the teacher or parents. For most students this is their first experience using specific problem solving strategies. Because of this, students will need time to experiment.

MODIFICATIONS

Because this unit is taught in small chunks, students of all abilities will be able to complete the daily and culminating assessments. The checklist will be used for all students but students will be assessed on an individual basis, not compared to the rest of their peers.
 
 

UNIT SCHEDULE/TIME PLAN

  This unit can be completed in 2 weeks when managed correctly. It is important however to be flexible if this is your student's first experience with this type of project. It is also important to plan more time then you feel will be necessary from your class if this is the first time you have tried this.

TECHNOLOGY USE

Students are required to complete a minimum of two problem solving experience during this unit. The may choose to use either the CD-ROM Mighty Math Number Heroes, where their work is kept directly in the computer or the may choose the web site activities Math Counts or Math For Kids (see attachments).

These are completed during the lessons. Students are able to use the computers AFTER the guided practice part of the lesson. By waiting until this part of the lesson, the teacher is able to o make sure that students understand the concepts taught.
    My suggestion would be to schedule students on computers so that students who will have more difficulty with the concepts will use the computer on a day where Make a List or Use an Object is taught. These are two of the easier strategies and they have a better chance of succeeding the first time with these, allowing them to use the computer.
   Two of the computer activities are assessed directly on the computer. One of the web sites has a teacher made handout that needs to be turned in.
 


REFLECTION

One of the problems that I would like to address is that of parent participation. Our parents were motivated by our workshop and therefore were anxious to participate. However, I know this is not always the case. For students who do not have a parent or guardian to participate, I would encourage a teacher to work in that leadership role. I would make sure this is done after school or during a recess period though.

We also send a certificate to both the student and the parent upon completion of the problem solving assessment.

 

Attachments

Guess and Check

#1

Craig, Kim and BeeAnn spent Saturday afternoon Christmas shopping. Craig spent twice as much as money as Kim and $25 less than BeeAnn. If the total amount of money they spent was $95.00, how much did each spend?

#2

The LeBlanc family took a four-day vacation. They drove the same distance on Friday and Monday, but only 1/8 as far on Saturday and 1/6 as far on Sunday. Total mileage of the trip was 66o miles. How many miles did they drive each day?

 

#3

In preparing for their class trip, fifth graders at SVB held four fundraising activities. The bake sale netted $76 more than the book sale and $124 more than the dance. The school carnival netted $320 more than the bake sale. If the total amount raised was $916.00, how much did the students raise on each activity?

#4

First 8 is added to me, then I am multiplied by 3, then 30 is subtracted from me, and finally I am divided by 10. The result is 18. What number am I?

 

 

Work Backwards

#1

At a recent diving competition, Meg's scores for her first three dives were 9.1, 9.6 and 9.9. To win the competition, she needs an average score of 9.5. What score does she need on her fourth and last event in order to win the gold medal?

#2

Kim gave a problem to Chris. She told him to pick a number, add 8 to it, triple that sum and then subtract 26. His answer was 67. What number did he pick?


#3

All of the houses on Uncle Sam's Drive are red, white or blue. There are twice as many white houses as red houses. There are 5 more red houses than blue houses. There are 7 blue houses. How many houses are there on Uncle Sam's Drive?

#4

The Oneida Basketball Team scores 100 or more points a game. In today’s games, Justin, Sam, Mark, and Michael do all of the scoring for the team. Sam scores 10 more points than Justin. Mark scores 9 fewer points than Sam. Michael scores twice as many points as Mark. At the end of the game, the highest scorer is Michael, with 42 points. How many points did the Oneida Basketball Team make?

#5

Hope, Kaylee, Morgan and Patrick are running for class president. Hope receives 40 more votes than Kaylee. Kaylee receives two-thirds as many votes as Morgan, and Morgan receives one-half as many votes as Patrick. Patrick receives exactly 60 votes. Who wins the election?

 

Find a Pattern

#2

The Clock is Ticking- After two minutes of a basketball game, The SVB Lakers were leading 8 to 3. If this pattern continued, what would the score be after 10 minutes?

#3

At the end of the game, the scorekeeper noticed an unusual pattern in the SVB Lakers scoring. The scores in the book showed that Player 1 scored 1 point. Player 3 scored 4 points. Player 5 scored 9 points. How many points did player number 9 score? How many did number 11 score?

#4

In a game, Chris took several different kinds of shots. First he would try a 2-point shot and then he would follow it with a three-point shot. How many points would Chris have scored if he attempted 20 shot and made every third try?

Make a List

#2

Soda Anyone?-Jolene puts 65 cents into the soda machine. The machine takes quarters, dimes and nickels. To buy a soda, Jolene must use exact change. What coins could she use to buy a soda?

#3

Checkerboard Fun-Using a checkerboard, determine how many squares of all sizes are on a checkerboard.

 

#4

Chris won trophies for his achievement in baseball, football and basketball. How many different ways can he arrange these in his trophy case?

 

#5

 Craig won a certificate for a free ice cream cone at the school fair. The cone is for a dynamite double scoop cone. He has 8 flavors that he can choose from. He refuses to get 2 scoops of the same flavor and he will not eat cookies and cream with orange sherbet. How many choices does Craig have for his cone?

 

Make a Table

#1 Award Winning Musicians-

Three children are each preparing to play their instrument in an upcoming concert. One child is a drum player. From the clues below, find the name of the child, their ages and what kind of instrument they are playing.

Clues:

 The child playing the drums is younger than BeeAnn.

 Kim is the oldest.

 The clarinet player is a girl.

 The kids are 10, 11 and 12.

 The instruments are the flute, clarinet and the drums.

#2- Collectors- Three children are each preparing a collection as part of a hobby show. One child collects Pokemon cards. Using the clues below, can you find the names of the children, their ages and what they collect?

 Sam is the oldest.

 The Pokemon collector is a girl.

 The child who collects Beanie Babies is younger than Chris.

 The Children's names are Sam, Chris, and Abby.

 They are 8. 9. And 10 years old.

 They collect Beanie Babies, Pokemon Cards and Pogs.

 

#3

Camera- If a camera takes 64 pictures every second, how many pictures does this camera take in ten minutes?

 

#4

Who is married to whom?-Chris, Craig, Tom and Steve are married to Kim, Lori, Bee and Melissa, although not necessarily in that order. Lori, who is Craig's sister, has four children. Chris and his wife have no children. Chris has never introduced his wife to Bee, who works late hours for Craig (but is not his wife; and Kim is considering telling Craig's wife to watch out). Craig and Tom are twin brothers. Who is married to whom?

 

#5

 Sue wants to make a play area for her children outside her home. She has 30 meters of fence that can be used to make the children's play area. How should Sue build the play space so that is has the biggest possible area? (Think area and perimeter) What are the dimensions of the biggest area? What shape is it?

 

Draw A Picture

 

#1

At the Sectional basketball game, there were two empty seats from every three seat that wee occupied. If there are 35 seats in the section, how many are empty? How many are full?

#2

The cheerleaders want to build a 4-layer pyramid for half time of the homecoming football game. They want to have 4 people on the bottom and one on the top. How many cheerleaders are needed to build the pyramid?

 

#3

The cheerleaders want to build a 7-layer pyramid for half time of the homecoming football game. They want to have 7 people on the bottom and one on the top. How many cheerleaders are needed to build the pyramid?

 

#4

On her bicycle trip, Sis started in Ozwald and rode through four other towns along County Route 1. Phido is twice as far from Ozwald as Joker was; Phido was also the same distance from Joker as it was from Sylvan Lake. Steamy River was only 3 miles beyond Phido. Name the towns Sis rode through in order.

#5

Shelly's mom wanted to do something special for her birthday. She decided she wanted to make her a soccer cake. Shelly's mom is not the best baker though, so she decided to make just a plain round cake, frost it white and then put soccer ball candies and flags around the edges. She placed the flags around the cake and between each, she but a candy ball. She put 14 balls on the cake. How many flags were there?

 

Use Objects

#4

Jason has a three-liter unmarked container, a five-liter unmarked container and an unlimited supply of Mountain Dew. He decided to share a little of his rootbeer with his friend Sal, but only 4 liters. How can he give Sal only four liters?

#5

Using a balance scale, you must be able to balance every whole kilogram amount from 1 kg through 15 kg. You may choose four standard weights to use, each a different number of kilograms. What weights will you use?

 

Problem Solving Strategies

Strategy

1-5 Difficulty

1-5 Usage

Pros

Cons

Guess and check

 

 

 

 

Make a List

 

 

 

 

Work Backward

 

 

 

 

Use Objects

 

 

 

 

Look for a Pattern

 

 

 

 

Draw A Picture

 

 

 

 

Make A Table

 

 

 

 

 

 

 Name _______________________ Date _____________________

 

 

Math For Kids

 

1.Log into the computer.

2.Type in http://prince.thinkquest.org/4471/

3.Choose Take the Challenge-try our word problems.

  1. Double click on this.
  2. Once the screen opens, choose any of the problems to start with.
  3. Record the problem you are going to solve on the bottom of this sheet.
  4. Then double click on the problem you want.
  5. Solve Parts 1-4. Record your answers on the bottom of this sheet.
  6. When you have completed the whole problem, click on GO TO ANSWER PAGE FOR THIS PROBLEM.
  7. Compare your answers to the correct answers. If you are right, double click on CHOOSE A DIFFERENT PROBLEM. If you miss a problem, RETURN TO PROBLEM # and try to figure out what you did wrong. Record the right answer next to your original.
  8. Once you have completed 10 problems, record your score at the bottom of this page.
  9. If you had difficulty with any problems, please give a brief written description of what happened on the back of this sheet. If not, GOOD GOING, I'll have to find something more difficult.

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NUMBER CORRECT ______ NUMBER ATTEMPTED 40

 

Name _____________________ DATE__________________________

Math Counts

  1. Log into the computer
  2. Type in http://mathcounts.org/Problems/problems/html
  3. Choose Problem of the Week.
  4. Double Click on this.
  5. Once the screen opens, scroll down until you see the problem of the week.
  6. Highlight the entire problem of the week and then copy it to your clipboard.
  7. Close the window, but not the program by clicking on the minimize line in the upper right hand corner of the screen.
  8. Open Word 97.
  9. Start a new document.
  10. Paste the problem into your new document.
  11. Once this is completed, use one of your problem solving strategies to solve the problem. You must include the solution and tan explanation of how you reached your answer.
  12. Save this under PROBLEM WEEK# ____ (fill in the date).
  13. I will check these on the computer. DO NOT PRINT!!!
  14. Once I have checked the problems, I will let you know and you can go into Word and see my comments and your grade. Please make any corrections and the save under 2 PROBLEM WEEK # _____ (fill in the date). This is how I will know to check corrections.